Effective polarized backscattering coefficients of a slightly rough surface to an EM beam

Analytical expressions of new effective like- and cross-polarized backscattering coefficients of a randomly slightly rough dielectric surface for an incident beam are given. They are the sum of the small perturbation solution as the beam is approximated as a plane wave and one or two modifying items resulting from the divergence of ray directions within the angle-width of the incident beam. For the like-polarizing case, one can usually neglect the angle-width effect of the beam, i.e., their two modifying items; for the cross-polarizing case one cannot. The results of numerical comparison of the new and previous theories with measurement for a randomly slightly rough soil surface support the new theory developed here. More direct experimental verification of the theory is expected to appear soon.<>